I've been having issues too. Over the past few months I (very rarely) have gotten both 503 and 404. I can hit refresh and the page will load.
Next time it happens I'll post time and url so you can check the logs.
Nope, it happens randomly. I've had it on all devices and the three different connections I use. One of my drivers also said it happened to him also but just once.
I'm wondering is this is a shared server, the host may have issues with resources being gobbled up from another site on the server, or it isn't configured right and a bunch of server side things are jamming it all up.